# Tensor renormalization group approach to two dimensional supersymmetric field theory by Ryo Sakai

**Nov 18, 2019 at 2:00 PM - 3:00 PM**

Rm 204 Physics Building

Tensor renormalization group approach to two dimensional supersymmetric field theory

by Ryo Sakai (University of Iowa)

Nov. 18th, 2-3pm, RM. 204

**Abstract:**

Monte Carlo simulations on discrete space-time lattices have been successful as a non-perturbative numerical approach to particle physics. However, many important models such as supersymmetric systems, chiral gauge theories, and finite density QCD have complex or negative Boltzmann weights, and Monte Carlo simulations cannot be simply applied to such models. This is a strong motivation to seek deterministic ways rather than Monte Carlo schemes, and tensor network is a powerful tool to break the situation. We discuss a coarse-graining algorithm for tensor networks and its application to a supersymmetric field theory. We put our focus on the two dimensional \mathcal {N=1}

Wess--Zumino model, which contains a one-component real scalar field and a two-component Majorana spinor field. While tensor network formulations for fermions can be constructed in a rather straightforward manner, scalar fields do not get along with tensor networks owing to the continuity. We discuss a new method to extract discrete tensor indices from the continuous scalar field. We show that our new formulation and the tensor renormalization group reproduce the analytical result of the Witten index.

Judah F Unmuth-Yockey (jfunmuth@syr.edu)